Weighted asymptotic korn and interpolation korn inequalities with singular weights

Davit Harutyunyan, Hayk Mikayelyan

Research output: Journal PublicationArticlepeer-review

1 Citation (Scopus)

Abstract

In this work we derive asymptotically sharp weighted Korn and Korn-like interpolation (or first and a half) inequalities in thin domains with singular weights. The constants K (Korn's constant) in the inequalities depend on the domain thickness h according to a power rule K = Chα, where C > 0 and α;∈ R are constants independent of h and the displacement field. The sharpness of the estimates is understood in the sense that the asymptotics hα is optimal as h → 0. The choice of the weights is motivated by several factors; in particular a spatial case occurs when making Cartesian to polar change of variables in two dimensions.

Original languageEnglish
Pages (from-to)3635-3647
Number of pages13
JournalProceedings of the American Mathematical Society
Volume147
Issue number8
DOIs
Publication statusPublished - 2019

Keywords

  • Korn inequality
  • Thin domains
  • Weighted Korn inequality

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics

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